But with Rondo being named captain this season, and with Danny Ainge remaining adamant that the Celtics, who host the Oklahoma City Thunder on Friday night, want to keep their four-time All-Star despite persistent rumors he’ll be traded, Rondo is considered the player around which the Celtics will build their future more than ever.

And that rhetoric again made the rounds Thursday when Ainge, the president of basketball operations, revealed the team discussed a contract extension with Rondo but was unable to get a deal done.

While Ainge said they indeed view Rondo as a “huge part” of the team and its future, he believes the aforementioned labels can also be misleading.

“Nobody is ‘the future of the franchise,’ ” Ainge told the Globe. “A franchise is bigger than any one individual. But we love him. That’s what [the extension offer] explains.”

Ainge initially disclosed the extension talks during his weekly appearance with 98.5 The Sports Hub, the team’s flagship radio station.

Rondo and his camp turned down the offer, but that was to be expected, as the NBA’s collective bargaining agreement limits the length and value of a possible extension at the moment.

As such, it would have been financially unwise for Rondo to accept an offer now when he stands to potentially make more this summer or even next summer when his current deal — a five-year extension worth $55 million he signed in the fall of 2009 — expires.

“I didn’t expect him to agree to it, and I understand why they didn’t,” Ainge said of the most recent extension offer. “We’ll continue to have talks when we can.”

It figures both sides will be focused on the summer of 2015, when Rondo will likely be one of the league’s top free agents on the market.

“He’ll be paid a lot,” Ainge said. “He’s a four-time All-Star. He’s 27 years old. He’ll be paid a lot, is my expectation.”

Make no mistake, the Celtics would like to keep Rondo, but Ainge doesn’t like the notion that the team must “build around” Rondo, or any one player for that matter.

“Everybody knows who the best players are on teams, but I just think that gives the players the impression that they’re more important than everybody else on the team and the rookies on the team. I just don’t like how that creates a culture of individualism as opposed to the whole team.

“[Rondo is] obviously a very important part of our team and has been for years. Some people are going to continue to use [those terms] whether I like it or not. I’m just saying I don’t like to use that.”

Ainge continued, “You look at LeBron James, who was a great player in Cleveland. He didn’t win a championship until he got with Dwyane Wade and with Chris Bosh [in Miami].

“Same thing with Paul, KG, and Ray — great, Hall of Fame, superstar players, they didn’t win until they got together with other people. The fact that you’re ‘building around’ one player or ‘he is the cornerstone’ — there’s only one or two of those guys in the history of the game, maybe a handful.

“I just want to sort of make that clear. Of course, we really like [Rondo]. We tried to extend him. He’s been a huge part of our team and will continue to be.“

The Celtics have stockpiled draft picks to help expedite their rebuilding process, but the question is what role Rondo will play in it.

“I don’t put too much on the future,” Rondo said recently.

But Ainge remains adamant the Celtics want to keep Rondo.

When asked if that message is understood across the league, Ainge pointed out he has had only one conversation with another team about Rondo.

“I actually did have a team call me and say, ‘Hey, would you have any interest in trading Rondo?’ Before he even offered me a package,” Ainge said. “And I said no. And that’s it. That’s as long as the conversation happened.

“Now, I did happen to know what that team had, and I happened to know that team’s assets. I can’t ever be put in a situation where the sentiment of my relationship with the player prevents me from doing what’s best for the franchise. But that’s the extent of it.”

Ainge continued, “And most of it is chatter. It’s just people, like I think recently, somebody, one of the national media guys, made a comment like, ‘Oh, I was talking with some NBA people on the road and they all think Danny is going to trade Rondo.’

“Well, it’s not like there’s a source. It’s just people that have their own opinion, sitting around, having a Diet Coke, talking about what I’m going to do with Rondo. Which is fine.

“That’s what they do. But then that sort of feeds itself.

“I think everybody knows how much we love Rondo. I don’t know how many times we have to say that.”

As the last man standing, Rondo is viewed as the team’s focal point, as the face of the Celtics.

Did he ever imagine this day would come?

“In this game, you never know,” Rondo said. “You never know where you’ll be.”

If the Celtics get their wish, Rondo will remain in Boston for years to come.

BostonGlobe.com complimentary digital access has been provided to you, without a subscription, for free starting today and ending in 14 days. After the free trial period, your free BostonGlobe.com digital access will stop immediately unless you sign up for BostonGlobe.com digital subscription. Current print and digital subscribers are not eligible for the free trial.

Thanks & Welcome to Globe.com

You now have unlimited access for the next two weeks.

BostonGlobe.com complimentary digital access has been provided to you, without a subscription, for free starting today and ending in 14 days. After the free trial period, your free BostonGlobe.com digital access will stop immediately unless you sign up for BostonGlobe.com digital subscription. Current print and digital subscribers are not eligible for the free trial.